To better understand the effect of an asperity on crack closure behavior, K-CMOD relations were examined using artificial asperity/ wedge, inserted into the fatigue crack in a three point bending specimen made of a hardened medium carbon steel. Experimental results revealed that the unloading phase of the K vs. CMOD curve exhibited a concave shape if soft artificial asperity (Al alloy) was inserted, signifying acceleration in the CMOD decrease at zero applied load. This was mainly related to elastic and plastic deformation in the wedge material during the unloading process. On the contrary, the linear unloading portion of K vs. CMOD was obtained as hard asperity (high carbon steel) was employed, which specified deceleration in the CMOD decrease at zero applied load, where the only elastic deformation in the asperity was affected. From their unloading curves, the severity of crack closure or ${Delta}K_{eff}$ value was found to be related to the strength of the asperity material. The values of ${Delta}K_{eff}$ were examined in two different ways, e.g., (i) the remote displacement method and (ii) the adjusted compliance ratio method (ACR). The ${Delta}K_{eff}$ value, measured using both approaches, decreases with increasing wedge strength, such as hardness and yield strength. The rate of reduction in ${Delta}K_{eff}$ was, however, changed depending on the manner of ${Delta}K_{eff}$ examination, in which the ${Delta}K_{eff}$ decreased at a higher rate for the compliance ratio method and at a lower rate for the remote displacement method. The reason for this is discussed in the present work.